Respuesta :
Step-by-step explanation:
- Assume that [tex]\log _{3}2[/tex] = [tex]\frac{p}{q}[/tex] ≥ 0 then p and q are positive integers
- So, it must comply with [tex]3^{p} = 2^{q}[/tex]
- If p and q are positive (≥ 0), then LHS is odd and RHS is even which is a clear contradiction.
- This shows that [tex]\log_{2}3[/tex] is irrational.
- Hence proved
